Resonant inverter employing frequency and phase modulation using optimal trajectory control

ABSTRACT

A series resonant inverter is controlled to provide a substantially constant output voltage to a load. The control utilizes a combination of optimal control methods and phase modulation to enable time optimal responses to changes in state of the system. State determinants (including resonant capacitor voltage, resonant inductor current, source voltage, and output load voltage) are continuously monitored, and an optimal control signal is generated therefrom. When operating within the operable frequency range of the inverter&#39;s controllable switch means, frequency is varied to maintain proper operation. When operating at an extremity of the operable frequency range, phase modulation is employed.

FIELD OF THE INVENTION

The present invention relates generally to resonant inverters. Moreparticularly, this invention relates to a series resonant inverter withimproved control which utilizes a method of optimal control incombination with phase modulation to maintain substantially constantoutput voltage over a wide range of operating conditions.

BACKGROUND OF THE INVENTION

Resonant inverters advantageously have low switching losses and lowswitching stresses. However, resonant operation is complex due to thefast dynamics of the high-frequency resonant tank circuit; and, hence,control is difficult. Disadvantageously, when input power or output loadconditions vary, output voltage or current control cannot be achievedthrough the use of usual control techniques. For example, one knownresonant inverter output load voltage or current control method is tovary the frequency of the rectangular wave signal supplied to theresonant circuit by the inverter via closed loop control. Commonlyassigned U.S. Pat. No. 4,541,041, issued on Sept. 10, 1985 to J. N. Parkand R. L. Steigerwald, which is hereby incorporated by reference,discloses in part such a frequency control technique. Briefly explained,the resonant nature of the circuit allows for control of output voltageor current through variation of the frequency at which the inverter'scontrollable switch means operate. Such a frequency control method hasbeen formed satisfactory under normal output load conditions forparticular types of resonant inverters (i.e., heavy or medium loadconditions for a series resonant inverter and light load conditions fora parallel resonant inverter). The drawback to frequency control,however, is that it may be inadequate to maintain a desired outputvoltage or current under extended output load conditions (i.e., light orno load conditions for a series resonant inverter and heavy loadconditions for a parallel resonant inverter).

In particular, frequency control of a series resonant inverter willnormally be adequate to maintain a desired output voltage during heavyor medium load conditions (i.e., low load resistance); that is, forheavy or medium load conditions, a series resonant circuit has a highquality factor Q and thus a good dynamic range of voltage or currentchange as frequency is varied. However, under extended or light outputload conditions (i.e., high load resistance) the series resonant circuitexhibits a low quality factor Q and thus only a small dynamic range ofoutput voltage or current change can be achieved as a function offrequency. As a result, for a series resonant inverter, it may beimpossible to maintain a desired output voltage or current under lightload and no load conditions solely with frequency control.

A resonant inverter control which provides an improved dynamic range ofoutput voltage or current control is disclosed in U.S. Pat. No.4,672,528, issued June 9, 1987 to J. N. Park and R. L. Steigerwald andassigned to the assignee of the present invention. This patent, which ishereby incorporated by reference, describes a resonant inverter which iscontrolled using either a frequency control mode or a phase shiftcontrol mode. In the frequency control mode, output voltage iscontrolled by varying the frequency of the rectangular wave signalsupplied to the resonant circuit within an operable range of thecontrollable switch means. Selecting means allows the control to operatein the phase shift control mode when the frequency of the rectangularwave signal is at an extremity of the operable range of the controllableswitch means.

Another method of resonant inverter control, which is derived fromoptimal control theory and state plane analysis, is presented in"Resonant Power Processors: Part II-Methods of Control" by RameshOruganti and Fred C. Lee, 1984 Industry Applications SocietyProceedings, pp. 868-878, and is hereby incorporated by reference.According to this method, hereinafter designated "optimal trajectorycontrol" to be described in detail below, each state trajectorycorresponds to particular values of instantaneous resonant tank energy,output voltage, output current and switching frequency. These statetrajectories are utilized to define a control law for the invertercontrol system which enables a series resonant inverter to respondquickly to load and control requirements. Disadvantageously, however, inthe method of "optimal trajectory control", as it presently exists, thecontrolled range of output voltages is limited in the same manner as thehereinabove described conventional frequency control method.

Accordingly, it is an object of the present invention to provide a newand improved resonant inverter exhibiting an improved dynamic range ofoutput load voltage control.

Another object of this invention is to provide a new and improvedresonant inverter control which utilizes a combination of optimalcontrol methods and phase modulation to maintain output load voltagesubstantially constant during all loading conditions.

Still another object of this invention is to provide a new and improvedresonant inverter control which switches automatically between differentcontrol means to maintain a substantially constant output load voltage.

Yet another object of the present invention is to provide an improvedmethod of controlling a resonant inverter in order to maintain a desiredoutput load voltage.

SUMMARY OF THE INVENTION

In accordance with the present invention, a new and improved resonantinverter is controlled using a combination of optimal trajectory controland phase modulation. In particular, optimal control means are employedto continuously monitor resonant capacitor voltage, resonant inductorcurrent, .[.rectangular wave voltage applied to the resonant tankcircuit.]. .Iadd.source voltage .Iaddend.and output load voltage,thereby determining the instantaneous "states" of the resonant inverter.A control law, defined in terms of state plane analysis, enablesmaintenance of stable operation on state trajectories corresponding toparticular values of the aforementioned state determinants. In this way,the improved control enables a time optimal response corresponding to achange in load conditions and, hence, a fast and efficient transitionbetween state trajectories.

For a series resonant inverter operating above resonance, there is amaximum frequency at which the controllable switch means can adequatelyfunction. When operating within the operable frequency range of thecontrollable switch means (i.e. below this maximum frequency and abovethe resonant frequency), a first control means provides frequencycontrol signals which frequency modulate the rectangular wave voltageapplied to the series resonant circuit so as to provide a constantoutput voltage and maintain stable operation. At an extremity of theoperable frequency range of the controllable switch means, invertercontrol automatically switches to a second control means. The secondcontrol means calculates a phase modulation angle corresponding to thedesired output voltage and generates a phase shift control signalrepresentative thereof. By thus combining a method of optimal controlwith phase modulation, a broader dynamic range of output load voltagecan be achieved under all operating conditions.

In another aspect of the present invention, a method is provided forcontrolling output load voltage through a combination of optimal controlmethods and phase modulation.

BRIEF DESCRIPTION OF THE DRAWINGS

The features and advantages of the present invention will becomeapparent from the following detailed description of the invention whenread with the accompanying drawings in which:

FIG. 1 is a schematic representation of a dc-to-dc converter including aseries resonant inverter;

FIG. 2 is a graphical illustration showing the magnitude of the outputvoltage plotted against the log of the frequency of the rectangular wavesignal supplied to the series resonant circuit employed in the inverterof FIG. 1 for heavy load, medium load, light load and no loadconditions;

FIG. 3 is a single state trajectory, state plane diagram for theresonant inverter of FIG. 1 operating above the resonant frequency;

FIG. 4a is a graphical representation of the rectangular wave voltageapplied to the series resonant inverter of FIG. 1;

FIG. 4b is a graphical representation of the phase modulated signal ofFIG. 4;

FIG. 5 is a graphical illustration showing the amplitude of the firstharmonic of the signal of FIG. 5 plotted against the phase modulationangle;

FIG. 6 is a functional block diagram of a resonant inverter controlsystem employing the series resonant inverter control of the presentinvention;

FIGS. 7a and 7b together comprise a functional block diagram of thepreferred embodiment of the resonant inverter control according to thepresent invention; and

FIGS. 8a-8i are graphical representations of output signals from certainelements comprising the block diagram of FIGS. 7a-7b in order toillustrate operation of the resonant inverter control 12 of the presentinvention.

DETAILED DESCRIPTION OF THE INVENTION

The improved resonant inverter control of the present invention will bedescribed with reference to the dc-to-dc converter shown in FIG. 1. Anexternal source (not shown) provides input dc voltage V_(s) to theconverter at terminals 10 and 11. Connected across terminals 10 and 11is a full bridge inverter 12 having four switching devices that arecapable of carrying reverse current and capable of being turned off by aswitching signal. The switching devices are illustrated as bipolarjunction transistors (BJTs) S1, S2, S3 and S4. Each respective switchingdevice has a diode D1, D2, D3 and D4 connected in inverse paralleltherewith, respectively. In operation above the resonant frequency, theswitching devices are turned on at zero current, and the inverseparallel diodes are commutated naturally. Hence, fast recovery diodesare not required. Moreover, other switching devices with gate turn-offcapability could be used instead of the BJTs, such as FETs each havingan integral parasitic diode for carrying reverse current or monolithicDarlington power transistors. It is further to be understood that thefull bridge inverter is illustrated for purposes of description only andthat the control technique of the present invention is not limited tosuch an inverter.

A series resonant tank circuit, comprising an inductor 14, a capacitor16, and the primary winding of an isolation transformer 18, is connectedbetween junctions a and b. The secondary winding of transformer 18 isconnected to the input of a full wave rectifier 20. The output of therectifier is connected in parallel with a filter capacitor 22 and anoutput load (not shown) across which the converter output voltage V_(o)is produced.

The resonant nature of the output load voltage of the inverter of FIG. 1is shown graphically in FIG. 2, where the magnitude of the output loadvoltage is plotted against the log of the frequency of the rectangularalternating voltage V_(ab) which is produced by inverter 12 and appliedacross the series resonant circuit. For proper power switchself-commutation, operation above the natural resonant frequency f_(r)is necessary. However, there is a maximum frequency f_(max) beyond whichthese switching devices will fail to operate satisfactorily. Thus, anoperable range OF of the switching devices is defined as that frequencyrange between f_(r) and f_(max). During medium or high output loadconditions, variation of frequency within this operable range OF issufficient to provide the desired output voltage or current control. Asillustrated graphically in FIG. 2, a desired converter output loadvoltage V_(d) may be maintained during heavy load and medium loadconditions by frequency control of the rectangular wave voltage V_(ab).However, during light load and theoretical no load conditions, variationof frequency within the operable range OF would be insufficient toattain the desired output load voltage V_(d). The present invention,therefore, employs a control technique for enhancing the dynamic rangeof converter output voltage control primarily needed under light load orno load conditions.

Within the operable frequency range OF of the controllable switchingdevices, the switches are controlled by a method of optimal trajectorycontrol. This method is derived from optimal control theory and stateplane analysis. In accordance therewith, the "control law" of the systemis determined by the desired state of the system. An instantaneous stateof the system is a function of resonant capacitor voltage, resonantinductor current. .[.voltage applied to the resonant tank circuit.]..Iadd.source voltage .Iaddend.and output load voltage. An instantaneousstate corresponds to a specific state trajectory. The desired statetrajectory, therefore, determines the control law of the system.

For operation above the resonant frequency f_(r), FIG. 3 illustrates astate plane diagram for the resonant inverter of FIG. 1. At the outsetof the ensuing state plane analysis, it is assumed that filter capacitor22 is sufficiently large such that the output voltage V_(o) remainsconstant during any single switching cycle interval As used herein, theterm "switching cycle interval" is defined as the time necessary totraverse a state trajectory. In FIG. 3, state trajectory 23 representsthe desired resonant inverter operation and corresponds to a particularoperating frequency and to specific values of the above-listed statedeterminants (i.e., resonant capacitor voltage, resonant inductorcurrent, .[.voltage applied to the resonant tank circuit.]. .Iadd.sourcevoltage.Iaddend., and output load voltage). Specifically, as atwo-dimensional state representation, the state trajectory is a plot ofZ_(o) i_(L) versus v_(C), where: Z_(o) =√L/C is the characteristicimpedance of the series resonant circuit; i_(L) represents resonantinductor .[.Current;.]. .Iadd.current .Iaddend.and v_(C) representsresonant capacitor voltage. Trajectory 23 comprises trajectory segmentsAB, BC, CD and DA corresponding to the conduction intervals of switchingdevices S1-S4 and diodes D1-D4. Each trajectory segment is a circulararc with a center and a radius determined by the state of the switchingdevices. For example, when switching devices S1 and S4 are conducting,current flows from node a through the series resonant circuit to node b,and the effective voltage applied to the series resonant circuit isV_(S) - V_(O). As a result, trajectory segment AB having center (V_(s)-V_(o), 0) represents the conduction interval of switching devices S1and S4. The remaining trajectory segment centers are similarlydetermined as follows.Iadd.:.Iaddend.trajectory segment BC having center(-V_(s) -V_(o), 0) represents the conduction interval for diodes D2 andD3; trajectory segment CD having center (-V_(s) +V_(o), 0) representsthe conduction interval for switching devices S2 and S3; and trajectorysegment DA having center (V_(s) +V_(o), 0) represents the conductioninterval for diodes D1 and D4.

As hereinabove discussed, the desired or optimal trajectory determinesthe control law of the system and, hence, the construction thereof.Besides the trajectory center, described hereinabove, another parametercharacterizing each trajectory segment is the trajectory radius R_(d)measured either from center (V_(s) +V_(o), O) or center (-V_(s) -V_(o),O). In operation, a control circuit computes radius R_(d) fromcontinuous measurements of the state determinants (i.e., resonantcapacitor voltage, resonant inductor current, .[.voltage applied to theresonant tank circuit.]. .Iadd.source voltage.Iaddend., and output loadvoltage). In this way, the control circuit maintains system operationcorresponding to the desired state trajectory by alternately switchingthe pairs of diagonally opposed switching devices. Moreover, when any ofthe state determinants changes, a control signal V_(CONTROL) generatedby an outer control loop, to be described hereinafter, enables thesystem to respond by making a time optimal transition to another steadystate trajectory.

In the article entitled "Implementation of Optimal Trajectory Control ofSeries Resonant Converters", by Ramesh Oruganti et al., 1987 PowerElectronics Specialty Conference Proceedings, pp. 451-459, which ishereby incorporated by reference, the control law for a resonantinverter operating below resonance is derived on pages 453-454 as:

    (R.sub.d V.sub.s).sup.2 =(V.sub.c +FV.sub.o -FV.sub.s).sup.2 +(i.sub.L Z.sub.o).sup.2,                                           (1)

where F is either +1 or -1, depending upon the sign of the inductorcurrent i_(L).

The control law of an inverter operating above resonance, such as thatof the present invention, may be similarly derived and may be expressedas:

    .[.(R.sub.d V.sub.s).sup.2 =(v.sub.c -FV.sub.o -FV.sub.s).sup.2 +(i.sub.L Z.sub.o).sup.2. .].

    (.Iadd.R.sub.d V.sub.s).sup.2 =(v.sub.c +FV.sub.o +FV.sub.s).sup.2 +(i.sub.L Z.sub.o).sup.2. .Iaddend.                       (2)

A resonant inverter control system constructed in accordance with thecontrol law of equation (2) advantageously enables time optimal controlof the switching devices when operating above resonance within theoperable frequency range thereof Disadvantageously, however, optimaltrajectory control according to .[.oruganti.]. .Iadd.Oruganti.Iaddend.et al. is limited to bi-level or frequency modulation. That is,as shown in FIG. 4A, the voltage applied to the resonant circuit is arectangular wave signal having two levels: +V_(S) and -V_(S). Usingoptimal trajectory control, frequency of the rectangular wave signal maybe varied to control output load voltage. Hence, like conventionalfrequency control methods, the control range of output voltage islimited as the frequency increases to the maximum operating frequency ofthe switching devices. The present invention, therefore, modifies andimproves the above-described optimal trajectory control system toprovide a new resonant control which yields a significantly increasedrange of controlled output load voltages under all loading conditions.In accordance therewith, the present invention combines optimaltrajectory control with phase modulation.

Since a series resonant circuit acts like a second order filter to therectangular wave voltage applied to the resonant tank circuit, as willbe appreciated by those of ordinary skill in the art, a usefulapproximation is that only the first harmonic of the rectangular wavesignal is applied to the resonant tank circuit. Further, if therectangular wave signal of FIG. 4A is phase modulated, then the phasemodulated signal takes the general trilevel form illustrated in FIG. 4B,where pulse width pw varies proportionately as the phase modulationangle φ. The fundamental harmonic F1 of this phase modulated signal isrepresented as:

    .[.F1=4πV.sub.s cosφ,.]. ##EQU1##

where φ=π/2×(1-2×pw/period), as shown in FIG. 4B, and φ is defined inunits of radians.

FIG. 5 is a graph of the magnitude of fundamental harmonic F1 versusphase modulation angle φ. As shown, for a 50% duty cycle (i.e., φ=0),the fundamental harmonic F1 is at its maximum value .[.4πV_(s) .]..##EQU2## As φ increases, the amplitude of the fundamental harmonicdecreases.Iadd.. .Iaddend.Therefore, phase modulation can be usedaccording to the present invention to decrease the amplitude of thefundamental harmonic of the voltage applied to the series resonantinverter. As a result, and as is evident from FIG. 2, a broader range ofcontrolled output load voltage may be obtained under all loadingconditions by decreasing the effective voltage applied to the seriesresonant circuit.

FIG. 6 is a block diagram illustrating a resonant inverter controlsystem employing the series resonant inverter control of the presentinvention. A commanded output voltage V_(REF) is compared to outputvoltage V_(o) by a summer 24. The resulting error signal V_(ERR) isinputted to a proportional plus integral (PI) compensator 26 whichgenerates control signal V_(CONTROL). Control signal V_(CONTROL) isprovided to series resonant inverter control 28 which drives inverter12. Control signals proportional to the aforementioned statedeterminants are also inputted to series resonant inverter control 28.These signals are represented as: k₁ i_(L), k₃ v_(c), k₃ V_(o), and k₃V₅, where k₁ and k₃ are constant scale factors to be describedhereinafter.

FIGS. 7a and 7b, connected at points 27 and 29, respectively, illustratethe preferred embodiment of the improved resonant inverter control 28 ofthe present invention. The control law of this improved system is amodification of the control law given by equation (2) to employ phasemodulation and is represented as:

    .[.(R.sub.d V.sub.s).sup.2 =(v.sub.c -FV.sub.o -FV.sub.s cos φ).sup.2 +(i.sub.L Z.sub.o).sup.2..].

    (.Iadd.R.sub.d V.sub.s).sup.2 =(v.sub.c +FV.sub.o +FV.sub.s cos φ).sup.2 +(i.sub.L Z.sub.o).sup.2. .Iaddend.          (4)

The state trajectory of the present invention (not shown), therefore, isa modification of that of FIG. 3 to account for the differences in aswitching cycle interval resulting from the application of phasemodulation to be described hereinafter.

Implementation of the control circuit according to the present inventioninvolves the use of sensing devices to detect instantaneous values ofstate determinants v_(c), i_(L), V_(s) and V_(o). Since these sensingdevices involve scaling to produce signals proportional to therespective state determinants, the following description, therefore,includes the aforementioned exemplary scale factors represented asconstants k₁ and k₃. For example, control signal k₁ i_(L), which isproportional to resonant inductor current, is derived from a suitablecurrent sensor 19. Typical current sensors are well known in the art andmany comprise, as examples: Hall effect current sensors, current sensingresistors, or current sensing transformers.

As shown in FIG. 7a, control signal k₁ i_(L) is applied to a comparator30. The output signal F of comparator 30 is either +1 or -1, dependingupon the sign of inductor current i_(L). The signal F is inputted tomultipliers 32 and 34, the value of F being the multiplicative factorthereof. The control signal k₁ i_(L) is also applied to a multiplier 36which performs a squaring operation to produce the signal k₂ (Z_(o)i_(L))², where Z_(o) =√L/C, a constant, is the characteristic impedanceof the series resonant circuit, and k₂ is also a constant.

Control signal k₃ V_(s), which is proportional to the applied sourcevoltage, is supplied by a source voltage sensor 21 to a multiplier 31which multiplies control signal k₃ V_(s) by cos φ, where φ is theaforementioned phase modulation angle value. Suitable voltage sensorsare well known in the art and may comprise, for example, a voltagedividing network of resistors. Signal k₃ V_(s) cos φ is applied tomultiplier 32 and is thereby multiplied by signal F.

Control signal k₃ V_(o), which is proportional to the output loadvoltage, is produced by a voltage sensor 23 and applied to multiplier 34to yield a signal Fk₃ V_(o). A summer 40 adds the signal Fk₃ V_(o) tostill another sensed control signal k₃ v_(c), which is sensed by avoltage sensor 25 and is proportional to the voltage across the resonantcapacitor. The resulting signal .[.k₃ (v_(c) -FV_(o)).]. .Iadd.k₃ (v_(c)+FV_(o)) .Iaddend.is added to the aforementioned signal Fk₃ V_(s) cos φby summer 42 to yield the signal .[.k₃ (v_(c) -FV_(o) -FV_(s) cos φ)..]..Iadd.k₃ (v_(c) +FV_(o) +FV_(s) cosφ). .Iaddend.The latter signal isinputted to a multiplier 44 which performs a squaring operation. Theresulting squared signal .[.k₂ (v_(c) -FV_(o) -FV_(s) cos φ)² .]..Iadd.k₂ (v_(c) +FV_(o) +FV_(s) cos φ)² .Iaddend. is added to thehereinabove derived signal k₂ (Z_(o) i_(L))² by a summer 46 and, asshown in FIG. 7b, is then inputted to gain amplifier 48 having thetransfer function -k₄ /k₂ where k₄ is a constant. The output ofamplifier 48 is a signal .[.-k₄ [(v_(c) -FV_(o) -FV_(s) cos φ)² +(Z_(o)i_(L))² ].]. .Iadd.-k₄ [(v_(c) +FV_(o) +FV_(s) cos φ)² +(Z_(o) i_(L))²].Iaddend., which is hereinafter referred to as the optimal controlsignal.

Control signal V_(CONTROL) is provided to a frequency modulationcontroller 50 and a phase modulation controller 52. The transferfunction of frequency modulation controller 50 is shown in FIG. 7b andmay be represented mathematically as: ##EQU3## where V_(F) is the outputvoltage of frequency modulation controller 50, V_(T) is a thresholdvoltage representing operation at an extremity of the operable frequencyrange for the controllable switch means, and C₁ is a constant. VoltageV_(F) is added in a summer 54 to the output signal of gain amplifier 48,and the result is inputted to the non-inverting input of a comparator56. The output signal from comparator 56 is supplied to a saw-toothgenerator 58.

The transfer function of phase modulation controller 52 is also shown inFIG. 7b and may be represented mathematically as: ##EQU4## where V.sub.φis the output voltage from phase modulation controller 52, V.sub.φ beingproportional to phase modulation angle φ, and C₂ is a constant. VoltageV.sub.φ is inputted to the inverting input of a comparator 60. Theoutput signal V_(G) of sawtooth generator 58 is supplied to thenoninverting input of comparator 60. Voltage V.sub.φ is also supplied tomultiplier 31 for which cos φ is the multiplicative factor.

The output signals CP1 and CP2 from comparators 56 and 60, respectively,provide the clock pulses for D-type (delay) flip-flops 62 and 64,respectively. As will be appreciated by those of skill in the art, sincethe signal at output D flip-flop 62 is supplied to the D1 input of Dflip-flop 62, D flip-flop 62 is a divide-by-two flip-flop; that is, theoutput frequency is one-half that of the clock frequency. The outputsignals from the D flip-flops control the base drive circuitry 65a-65dfor the respective switching devices S1-S4. Suitable base drivecircuitry is well-known in the art.

In operation, since the output signal from comparator 56 which providesclock pulses to the divide-by-two D flip-flop 62 also drives sawtoothgenerator 58, the sawtooth generator produces a voltage ramp signalV_(G) operating at twice the frequency of gate drive circuitry 65a-65d.In particular, the voltage ramp signal V_(G) resets to zero each timethe output signal at Q1 of D flip-flop 62 transitions from logic level 0to 1 or 1 to 0. The output ramp voltage of sawtooth generator 58 iscompared with voltage V.sub.φ by comparator 60 which provides clockpulses for D flip-flop 64. For a positive edge triggered D flip-flop 64,for example, when the output signal of comparator 60 transitions from alow logic level to a high logic level, the signal at output Q2 ofD-flip-flop 64 latches to the same value as the signal at output Q1 of Dflip-flop 62.

For V_(CONTROL) <V_(T), the output voltage V_(F) of frequency modulationcontroller 50 is C₁ V_(CONTROL), and the output voltage V.sub.φ of phasemodulation controller 52 is zero, thus indicating that phase modulationangle φ=0. Therefore, since the value of phase modulation angle φ isprovided to multiplier 31, and cos φ=1 for φ=0, there is no phasemodulation. On the other hand, there is frequency modulation. That is,the output voltage C₁ V_(CONTROL) of frequency modulation controller 50is added to the output signal of summing amplifier 48 and applied to thenon-inverting input of comparator 56. The output signal CP1 ofcomparator 56 provides clock pulses to D flip-flop 62 to toggle itsstate and, as stated above, also drives sawtooth generator 58. Theoutput voltage .[.V_(c) .]. .Iadd.V_(G) .Iaddend.of the sawtoothgenerator is compared with voltage V.sub.φ =0 by comparator 60 whichprovides clock pulses CP2 to D flip-flop 64. As a result, D flip-flop 64is toggled almost simultaneously with D flip-flop 62. In this way, forV_(CONTROL) <V_(T), frequency modulation using optimal control isachieved when operating within the operable frequency range of theswitching devices.

For V_(CONTROL) ≧V_(T), the output voltage V_(F) of frequency modulationcontroller 50 is C₁ V_(T), a constant, so that the switching frequencyof switching devices S1, S2, S3 and S4 is fixed at an extremity of theoperable frequency range thereof. Under these conditions, the outputvoltage V.sub.φ of phase modulation controller 52 is C₂ (V_(CONTROL)-V_(T)). This voltage V.sub.φ is compared with the output signal V_(G)of sawtooth generator 58 by comparator 60. As a result, the clock pulsesCP2 from comparator 60 to D flip-flop 64 are delayed by an amount oftime proportional to phase modulation angle φ. Voltage V.sub.φ alsoenables multiplier 31 to multiple source voltage V_(S) by cos φ. In thisway, phase modulation is employed to produce the tri-level voltagewaveform shown in FIG. 4B for controlling the series resonant inverter.By thus combining a method of optimal trajectory control with phasemodulation, a broader dynamic range of output load voltage can beachieved under all operating conditions.

FIGS. 8a-8i are waveforms that illustrate in detail the operation of thenew resonant inverter control for a specific case of V_(CONTROL) >V_(T).For simplicity, assume the output signal CP1 of comparator 56 has aconstant pulse width and is represented by the signal of FIG. 8a. For apositive edge-triggered D flip-flop 62, the output signals at Q1 and Q1respectively, are illustrated in FIGS. 8b and 8c, respectively. Voltageramp signal V_(G) from sawtooth generator 58, which is reset each timethe output signals from D flip-flop 62 change state, is shown in FIG.8d. Voltage V.sub.φ, which determines the phase modulation angle φ, isillustrated as a voltage between 0 and 10 V in FIG. 8e. For thisexample, voltage V.sub.φ =5 V. The output signal CP2 of comparator 60,determined by comparing voltage V.sub.φ with the output ramp voltageV_(G) of sawtooth generator 58, is represented in FIG. 8f andconstitutes clock pulses for D flip-flop 64. For a positiveedge-triggered D flip-flop 64, the output signals at Q2 and .[.Q2.]..Iadd.Q2 .Iaddend.respectively, are illustrated in FIGS. 8g and 8h,respectively. The flip-flop output signals at Q1, .[.Q1.]..Iadd.Q1.Iaddend., Q2 and .[.Q2.]. .Iadd.Q2.Iaddend., respectively,control the base drive circuitry 65a-65 d, respectively, and produce asa result the tri-level phase modulated signal shown in FIG. 8i. FromFIG. 8i and the equation for phase modulation angle φ given hereinabove,it can be seen that phase modulation angle φ=π/4 radians for thisexample.

While the preferred embodiments of the present invention have been shownand described herein, it will be obvious that such embodiments areprovided by way of example only. Numerous variations, changes andsubstitutions will occur to those of skill in the art without departingfrom the invention herein. Accordingly, it is intended that theinvention be limited only by the spirit and scope of the appendedclaims.

What is claimed is:
 1. An improved dc-to-dc converter, comprising:aresonant inverter having two pairs of controllable switch means, theswitch means of each pair being connected in series and each pair of theseries-connected switch means being adapted to be connected in parallelacross an external dc supply; a series resonant circuit connectedbetween the junctions of said controllable switch means and comprising acapacitor and an inductor, said inverter being adapted to apply arectangular wave voltage to said series resonant circuit; a full waverectifier inductively coupled to said series resonant circuit, theoutput of said rectifier being adapted to supply a substantiallyconstant preselected output voltage to a load; state determinant sensingmeans for continuously monitoring converter state determinantscomprising voltage across said capacitor, current through said inductor,the .[.rectangular wave voltage applied to said series resonantcircuit.]. .Iadd.dc supply voltage.Iaddend., and the output voltage;optimal control means responsive to said state determinant sensing meansfor generating an optimal control signal corresponding to theinstantaneous values of said state determinants; first control meansresponsive to said optimal control signal for controlling the outputvoltage by frequency modulating the rectangular wave voltage applied tosaid series resonant circuit so as to maintain stable operation of saidseries resonant circuit when the operating frequency of saidcontrollable switch means is within the operable frequency rangethereof; and second control means responsive to said optimal controlsignal for controlling the output voltage by providing a phasemodulation angle signal for phase modulating the rectangular wavevoltage applied to said series resonant circuit and modifying saidoptimal control signal .Iadd.in .Iaddend.accordance therewith so as tomaintain stable operation .Iadd.of .Iaddend.said series resonant circuitwhen the operating frequency of said controllable switch means is at anextremity of the operable frequency range thereof.
 2. The improvedconverter of claim 1, further comprising:frequency measuring meanscoupled to the output of said inverter for determining when theoperating frequency of said controllable switch means is at an extremityof the operable range thereof.
 3. The improved converter of claim 1wherein said first control means comprises:frequency modulation meansfor generating a frequency modulation signal; comparison means forcomparing said frequency modulation signal with said optimal controlsignal and for generating a difference signal resulting therefrom; andfrequency control means responsive to said difference signal forgenerating a frequency control signal for varying the operatingfrequency of said controllable switch means.
 4. The improved converterof claim 3, further comprising:sawtooth generator means responsive tosaid frequency control signal for generating a ramp voltage; secondcomparison means for comparing said ramp voltage with said phasemodulation angle signal; and flip-flop means responsive to saidfrequency control signal and to the output signal of said secondcomparison means, said flip-flop means being coupled to saidcontrollable switch means for providing control signals to vary theoperating frequency of said controllable switch means when operatingwithin the operable frequency range thereof and to phase modulate therectangular wave voltage when operating at an extremity of the operablefrequency range.
 5. .[.At.]. .Iadd.An .Iaddend.improved control for aresonant inverter, said inverter including a series resonant circuitwhich comprises a capacitor and an inductor, said inverter furtherincluding controllable switch means for producing a rectangular.[.are.]. .Iadd.wave .Iaddend.voltage .Iadd.when coupled to an externaldc supply .Iaddend.and applying said voltage to said series resonantcircuit, the output of said resonant inverter providing a substantiallyconstant output voltage to a load, said improved controlcomprising:state determinant sensing means for continuously monitoringconverter state determinants comprising voltage across said capacitor,current through said inductor, the .[.rectangular wave voltage andapplying said voltage applied to said series resonant circuit.]..Iadd.dc supply voltage.Iaddend., and the output voltage; optimalcontrol means responsive to said state determinant sensing means forgenerating an optimal control signal corresponding to the instantaneousvalues of said state determinants; first control means responsive tosaid optimal control signal for controlling the output voltage byfrequency modulating the rectangular wave voltage applied to said seriesresonant circuit so as to maintain stable operation of said seriesresonant circuit when the operating frequency of said controllableswitch means is within the operable frequency range thereof; and second.[.controls.]. .Iadd.control .Iaddend.means responsive to said optimalcontrol signal for controlling the output voltage by providing a phasemodulation angle signal for phase modulating the rectangular wavevoltage applied to said series resonant circuit and modifying saidoptimal control signal in accordance therewith so as to maintain stableoperation of said series resonant circuit when the operating frequencyof said controllable switch means is at an extremity of the operablefrequency range thereof.
 6. The improved control of claim 5, furthercomprising:frequency measuring means coupled to the output of saidinverter for determining when the operating frequency of saidcontrollable switch means is at an extremity of the operable rangethereof.
 7. The improved control of claim 5 wherein said first controlmeans comprises:frequency modulation means for generating a frequencymodulation signal; comparison means for comparing said frequencymodulation signal with said optimal control signal and for generating adifference signal resulting therefrom; and frequency control meansresponsive to said .[.differences.]. .Iadd.difference .Iaddend.signalfor generating a frequency control signal for varying the operatingfrequency of said controllable switch means.
 8. The improved control ofclaim 7, further comprising:sawtooth generator means responsive to saidfrequency control signal for generating a ramp voltage; secondcomparison means for comparing said ramp voltage with said phasemodulation angle signal; and flip-flop means responsive to saidfrequency control signal and to the output signal of said secondcomparison means, said flip-flop means being coupled to saidcontrollable switch means for providing control signals to vary theoperating frequency of said controllable switch means when operatingwithin the operable frequency range thereof and to phase modulate therectangular wave voltage when operating at an extremity of the operablefrequency range.
 9. A method for controlling a resonant inverter, saidinverter having controllable switch means for producing a rectangularwave signal .Iadd.when coupled to an external dc supply .Iaddend.andapplying said signal to a series resonant circuit which comprises acapacitor and an inductor, the output of said resonant inverterproviding a substantially constant output voltage to a load, saidcontrol method comprising the steps of:continuously monitoring statedeterminants comprising voltage across said capacitor, current throughsaid inductor, .[.said rectangular wave signal.]. .Iadd.the dc supplyvoltage.Iaddend., and said output voltage; generating an optimal controlsignal corresponding to a predetermined combination of the instantaneousvalues of said state determinants; frequency modulating said rectangularwave signal applied to said series resonant circuit so as to maintainstable operation of said series resonant circuit when the operatingfrequency of said controllable switch means is within the operablefrequency range thereof; and generating a phase modulation angle signalfor phase modulating said rectangular wave signal and modifying saidoptimal control signal in accordance therewith so as to maintain stableoperation of said series resonant circuit when the operating frequencyof said controllable switch means is at an extremity of the operablefrequency range thereof.